Non-simple magnetothermoelastic solid cylinder with variable thermal conductivity due to harmonically varying heat

The model of two-temperature magneto-thermoelasticity for a non-simple variable-thermalconductivity infinitely-long solid cylinder is established. The present cylinder is made of an isotropic homogeneous thermoelastic material and its bounding plane is traction-free and subjected to a timedependent temperature. An exact solution is firstly obtained in Laplace transform space to obtain the displacement, incremental temperature, and thermal stresses. The inversion of Laplace transforms has been carried out numerically since the response is of more interest in the transient state. A detailed analysis of the effects of phase-lags, an angular frequency of thermal vibration and the variability of thermal conductivity parameter on the field quantities is presented.